# A simple microstructure return model explaining microstructure noise and Epps effects

**Authors:** A. Saichev, D. Sornette  
**arXiv:** [1202.3915](https://arxiv.org/abs/1202.3915)  
**Date:** 2012-02-17  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1202.3915v1/

## Key points

- Saichev and Sornette present a comprehensive model of financial returns that incorporates various factors such as the ARFIMA process, bid-ask bounce effect, fat tail distribution of returns, and non-Poissonian statistics of inter-trade intervals.
- The authors use this model to explain important stylized facts observed in the statistics of microstructure returns, including short-ranged correlation of returns, long-ranged correlations of absolute returns, microstructure noise, and Epps effects.
- Microstructure noise effect states that volatility is a decreasing function of the time scale used to estimate it. This paradoxical phenomenon is explained by the negative return correlations inherent in the definition of the bid-ask bounce component.
- The Epps effect states that cross-correlations between asset returns are increasing functions of the time scale at which they are estimated. In cases where there is a genuine correlation between two assets' returns, this effect is attributed to an average statistical overlap of momentum defined over a finite time scale in the presence of a long memory process.
- The authors' model allows them to explain both qualitatively and quantitatively important stylized facts observed in the statistics of microstructure returns.
- Their work has implications for investors who seek to understand market dynamics better and make more informed investment decisions based on these insights.

## Summary

In their paper titled "A simple microstructure return model explaining microstructure noise and Epps effects," A. Saichev and D. Sornette present a comprehensive model of financial returns that incorporates various factors such as the ARFIMA process, bid-ask bounce effect, fat tail distribution of returns, and non-Poissonian statistics of inter-trade intervals. The authors use this model to explain important stylized facts observed in the statistics of microstructure returns, including short-ranged correlation of returns, long-ranged correlations of absolute returns, microstructure noise, and Epps effects. The microstructure noise effect states that volatility is a decreasing function of the time scale used to estimate it. This paradoxical phenomenon is explained by the negative return correlations inherent in the definition of the bid-ask bounce component. On the other hand, the Epps effect states that cross-correlations between asset returns are increasing functions of the time scale at which they are estimated. In cases where there is a genuine correlation between two assets' returns, this effect is attributed to an average statistical overlap of momentum defined over a finite time scale in the presence of a long memory process. The authors' model allows them to explain both qualitatively and quantitatively important stylized facts observed in the statistics of microstructure returns. They show how their model can account for short-ranged correlation of returns, long-ranged correlations of absolute returns, microstructure noise and Epps effects. By combining these different factors into one comprehensive model, Saichev and Sornette provide valuable insights into how financial markets operate at a microscopic level. Their work has implications for investors who seek to understand market dynamics better and make more informed investment decisions based on these insights.